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Chapter 13 Inference for Tables: Chi-Square Procedures

Chapter 13 Inference for Tables: Chi-Square Procedures. AP Statistics 13 – Chi-Square Tests. Chi-Square Procedures. Ch 12: Comparing 2 population proportions Chi-Square Tests: 1. Goodness of Fit – examining the distribution of proportions within a single population (13.1)

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Chapter 13 Inference for Tables: Chi-Square Procedures

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  1. Chapter 13Inference for Tables: Chi-Square Procedures AP Statistics 13 – Chi-Square Tests

  2. Chi-Square Procedures • Ch 12: Comparing 2 population proportions • Chi-Square Tests: • 1. Goodness of Fit – examining the distribution of proportions within a single population (13.1) • 2. Homogeneity of Populations – 2 or more (13.2) population proportions (2-way tables  Matrices) • 3. Association/Independence – Matrices  (13.2) (determine whether the distribution of one variable has been influenced by another)

  3. Then we could perform additional tests of significance for each of the remaining colors. • Very Inefficient! • Chi-Square ( ) test for goodness of fit.

  4. Properties of Chi-Square Distributions • Family of distributions that take only positive values and are Skewed Right! • A specific Chi-Square Distribution is specified by one parameter • Degrees of Freedom! • Area under the curve = 1 • Table E (in back of our book)

  5. Conditions • Null Hyp: the actual population proportions are EQAUL to the hypothesized proportions. • Alternative Hyp: DIFFERENT • The sample was obtained randomly (SRS) • All Expected counts are at least 1 • No more than 20% of the Expected counts are less than 5

  6. Goodness of Fit - Most commonly used in field of Genetics • Example 13.2: Mating 2 Red-Eyed Fruit Flies • Mate 2 fruit flies having genetic makeup RrCc • R – Red eyes r – white eyes • C – Curly wings c – straight wings • Punnett Square baby! • Of 200 offspring: 101 RC, 42 Rc, 49 rC, 8 rc • Do these data differ significantly from what the biologist predicted?

  7. 13.2 – Inference for Two-way tables • Now, we can compare more than 2 groups • Use Chi-Square test for Homogeneity of populations • Chi-Square test for Association/Independence – Use for 2 classifications, 2 categorical variables. • H(0): There is NO ASSOCIATION b/w the 2 variables. • Note: • df for a two-way table: (rows - 1)x(columns - 1)

  8. Are these data good evidence that the proportions of successes for the three treatments differ in the population of all cocaine users?

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